On the computational aspects of Charlier polynomials
Charlier polynomials (CHPs) and their moments are commonly used in image processing due to their salient performance in the analysis of signals and their capability in signal representation. The major issue of CHPs is the numerical instability of coefficients for high-order polynomials. In this stud...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2020-01-01
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| Series: | Cogent Engineering |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/23311916.2020.1763553 |
| _version_ | 1797760295510212608 |
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| author | Alaa M. Abdul-Hadi Sadiq H. Abdulhussain Basheera M. Mahmmod |
| author_facet | Alaa M. Abdul-Hadi Sadiq H. Abdulhussain Basheera M. Mahmmod |
| author_sort | Alaa M. Abdul-Hadi |
| collection | DOAJ |
| description | Charlier polynomials (CHPs) and their moments are commonly used in image processing due to their salient performance in the analysis of signals and their capability in signal representation. The major issue of CHPs is the numerical instability of coefficients for high-order polynomials. In this study, a new recurrence algorithm is proposed to generate CHPs for high-order polynomials. First, sufficient initial values are obtained mathematically. Second, the reduced form of the recurrence algorithm is determined. Finally, a new symmetry relation for CHPs is realized to reduce the number of recurrence times. The symmetry relation is applied to calculate $$ \sim $$50% of the polynomial coefficients. The performance of the proposed recurrence algorithm is evaluated in terms of computational cost and reconstruction error. The evaluation involves a comparison with existing recurrence algorithms. Moreover, the maximum size that can be generated using the proposed recurrence algorithm is investigated and compared with those of existing recurrence algorithms. Comparison results; indicate that the proposed algorithm exhibits better performance because it can generate a polynomial 44 times faster than existing recurrence algorithms. In addition, the improvement of the proposed algorithm over the traditional recurrence algorithms in terms of maximum-generated size is between 19.25 and 42.85. |
| first_indexed | 2024-03-12T18:56:32Z |
| format | Article |
| id | doaj.art-82d9d7d34c6340e2a90c3fd692ccc7d0 |
| institution | Directory Open Access Journal |
| issn | 2331-1916 |
| language | English |
| last_indexed | 2024-03-12T18:56:32Z |
| publishDate | 2020-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Cogent Engineering |
| spelling | doaj.art-82d9d7d34c6340e2a90c3fd692ccc7d02023-08-02T06:53:06ZengTaylor & Francis GroupCogent Engineering2331-19162020-01-017110.1080/23311916.2020.17635531763553On the computational aspects of Charlier polynomialsAlaa M. Abdul-Hadi0Sadiq H. Abdulhussain1Basheera M. Mahmmod2University of BaghdadUniversity of BaghdadUniversity of BaghdadCharlier polynomials (CHPs) and their moments are commonly used in image processing due to their salient performance in the analysis of signals and their capability in signal representation. The major issue of CHPs is the numerical instability of coefficients for high-order polynomials. In this study, a new recurrence algorithm is proposed to generate CHPs for high-order polynomials. First, sufficient initial values are obtained mathematically. Second, the reduced form of the recurrence algorithm is determined. Finally, a new symmetry relation for CHPs is realized to reduce the number of recurrence times. The symmetry relation is applied to calculate $$ \sim $$50% of the polynomial coefficients. The performance of the proposed recurrence algorithm is evaluated in terms of computational cost and reconstruction error. The evaluation involves a comparison with existing recurrence algorithms. Moreover, the maximum size that can be generated using the proposed recurrence algorithm is investigated and compared with those of existing recurrence algorithms. Comparison results; indicate that the proposed algorithm exhibits better performance because it can generate a polynomial 44 times faster than existing recurrence algorithms. In addition, the improvement of the proposed algorithm over the traditional recurrence algorithms in terms of maximum-generated size is between 19.25 and 42.85.http://dx.doi.org/10.1080/23311916.2020.1763553orthogonal polynomialscharlier polynomialscharlier momentsrecurrence algorithm |
| spellingShingle | Alaa M. Abdul-Hadi Sadiq H. Abdulhussain Basheera M. Mahmmod On the computational aspects of Charlier polynomials Cogent Engineering orthogonal polynomials charlier polynomials charlier moments recurrence algorithm |
| title | On the computational aspects of Charlier polynomials |
| title_full | On the computational aspects of Charlier polynomials |
| title_fullStr | On the computational aspects of Charlier polynomials |
| title_full_unstemmed | On the computational aspects of Charlier polynomials |
| title_short | On the computational aspects of Charlier polynomials |
| title_sort | on the computational aspects of charlier polynomials |
| topic | orthogonal polynomials charlier polynomials charlier moments recurrence algorithm |
| url | http://dx.doi.org/10.1080/23311916.2020.1763553 |
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